Abstract: This study investigated the cooperative optimal preview tracking problem of discrete-time multi-agent systems under the assumption of the communication topology containing a directed spanning tree. First, a state augmentation technique was used to convert the cooperative preview tracking problem into a global optimal regulation problem of an augmented system. Second, by resorting to relative conclusions about the discrete-time linear quadratic regulation theory, an optimal controller was obtained, which can guarantee the asymptotic stability of the closed-loop augmented system. Moreover, a global optimal preview controller was provided in order for the original system to achieve the tracking consensus. Finally, the simulation results not only verified the effectiveness of the designed controller, but also indicated that it is critical for accurately tracking the reference signal to moderately increase the preview length.